The idea that LSD is a true property of physical theories can be
traced back to causality, or the statement that the amplitude cannot
grow too fast in the Regge limit. Otherwise we could have simply added
a tree-level exchange by a large-spin particle which would contribute
to a given spin partial wave. Due to causality we cannot do
this (see e.g. Ref. [1]}). The situation is particularly dramatic in gravity. In this
case the only particle that can be exchanged at tree-level in graviton
scattering without violating causality is the graviton itself.
Moreover, its self-coupling has to be the one of Einstein gravity Ref. [1]}, [3]}, [4]}, [5]}
. Alternatively, particles of all spins have
to be exchanged at tree level to preserve causality, which is the
mechanism realized in string theory. It is important to emphasize
that at the level of \(2 \rightarrow 2\)  scattering LSD does not follow from
causality and we do not prove it in this paper, rather we use it as a
principle to organize the known data, and suggest that it may hold
more generally. It would be interesting to understand if it follows
from considerations on the consistency of \(n \rightarrow m\)  graviton
scattering.
